In a tug-of-war, three men pull on a rope to the left at A and three men pull to the right at B with forces of equal magnitude. Now a 5-lb weight is hung vertically from the center of the rope. (a) Can the men get the rope AB to be horizontal? (b) If not, explain. If so, determine the magnitude of the forces required at A and B to do this.

(a) No, the men can never get the rope AB to be horizontal.
(b) If the object is in vertical equilibrium, the sum of the forces in the vertical direction must be zero, that is

The weight of the object to make the rope horizontal is zero, but as given in the question the weight of the object is 5-lb.
This proves that the men can never make the rope horizontal again if the object has a weight of 5-lb.